Eevee Transparency gradient
Here is a node setup to achieve the transparent gradient sphere effect:




I'm using a Mapping node to control the direction of the gradient, Gradient Texture node for the gradient itself, and a ColorRamp node to control the transition. For the transparent part of the object, I'm using a glass shader with IOR very close to 1 (or it will look like real glass), and 0.6 roughness to make the object behind appear more blurry.

And make sure you enable screen space refraction in both render and material settings, or the transparency won't render correctly.

I don't know why you are trying to avoid using textures. While this procedural setup works well on a sphere, I don't think it will work if you are going to apply it to something more complex (like a frog model). Since it's using a simple linear gradient, it's very hard to make it fit perfectly on the frog's chin. I would recommend using texture painting if you really want to do that.